- Problems[[Student version, January 17, 2003]] 439
Problems
11.1Heart failure
Amuscle cell normally maintains a very low interior calcium concentration; Section 12.4.2 will
discuss how a small increase in the interior [Ca2+]causes the cell to contract. To maintain this low
concentration, muscle cells actively pump out Ca2+.The pump used by cardiac (heart) muscle is
an antiport (Section 11.3.5): It couples the extrusion of calcium ions to the entry into the cell of
sodium.
The drug oubain suppresses the activity of the sodium–potassium pump. Why do you suppose
this drug is widely used to treat heart failure?
11.2Electrochemical equilibrium
Suppose we have a patch of cell membrane stuck on the end of a pipette (tube). The membrane is
permeable to bicarbonate ions, HCO− 3 .Onside A we have a big reservoir with bicarbonate ions at
aconcentration of 1M;onside B there’s a similar reservoir with a concentration of 0. 1 M.Nowwe
connect a power supply across the two sides of this membrane, to create a fixed potential difference
∆V=VA−VB.
a. What should ∆Vbein order to maintain equilibrium (no net ion flow)?
b. Suppose ∆V= 100 mV.Which way will bicarbonate ions flow?
11.3Vacuole equilibrium
Here are some data for the marine alga Chætomorpha. The extracellular fluid is seawater;
the “plasmalemma” (outer cell membrane) separates the outside from the cytoplasm; a second
membrane (“tonoplast membrane”) separates the cytoplasm from an interior organelle, the vacuole
(Section 2.1.1 on page 34). (In this problem we pretend that there are no other small ions than
the ones listed here.)
Ion Vacuole Cytoplasm Extracellular VNernst(plasmalemma) VNernst(tonoplast)
(mM)(mM)(mM)(mV)(mV)
K+ 530 425 10? − 5. 5
Na+ 56 50 490 +57?
Cl− 620 30 573 − 74 +76a. The table gives some of the Nernst potentials across the two membranes. Fill in the missing
ones.
b. The table does not list the charge densityρq,macroarising from impermeant macroions in the
cytoplasm. What is−ρq,macro/einmM?
c. The actual measured membrane potential difference across the tonoplast membrane is +76mV.
Suppose all the quoted numbers are accurate to about 2%. Which ion(s) must be actively pumped
across the tonoplast membrane, and in which direction(s)?
d. Suppose we selectively shut down the ion pumps in the tonoplast membrane, but the cell
metabolism continues to maintain the listed concentrations in the cytoplasm. The system then
relaxes to a Donnan equilibrium across the tonoplast membrane. What will be the approximate
ion concentrations inside the vacuole, and what will be the final Donnan potential?
11.4 T 2 Relaxation to Donnan equilibrium
Explore what happens to the resting steady state (see Section 11.1.3) after the ion pumps are
suddenly turned off, as follows.